Coprime facts for kids

In mathematics, two whole numbers are called coprime (or relatively prime) if they don't share any common factors other than 1. Think of it this way: if you can't find any number (except 1) that divides both of them perfectly, then they are coprime. This means their greatest common divisor (GCD), which is the biggest number that divides both of them, is exactly 1.

What are Coprime Numbers?

Understanding Factors

To understand coprime numbers, let's first talk about factors. A factor is a number that divides another number exactly, with no remainder. For example, the factors of 6 are 1, 2, 3, and 6. The factors of 35 are 1, 5, 7, and 35.

Coprime Examples

Let's look at 6 and 35.

• The factors of 6 are 1, 2, 3, 6.
• The factors of 35 are 1, 5, 7, 35.

The only number that divides both 6 and 35 is 1. So, 6 and 35 are coprime.

Now, consider 6 and 27.

• The factors of 6 are 1, 2, 3, 6.
• The factors of 27 are 1, 3, 9, 27.

Both 6 and 27 can be divided by 1 and 3. Since they share a common factor (3) other than 1, they are not coprime.

Here's another example with 4 and 5:

• 4 can be written as 2 × 2 × 1. Its factors are 1, 2, 4.
• 5 can be written as 5 × 1. Its factors are 1, 5.

The only common factor is 1. So, 4 and 5 are coprime.

And for numbers that are not coprime, like 10 and 5:

• 10 can be written as 5 × 2. Its factors are 1, 2, 5, 10.
• 5 can be written as 5 × 1. Its factors are 1, 5.

They share common factors 1 and 5. Since they share 5 (which is not 1), they are not coprime.

Cool Facts About Coprime Numbers

• Prime numbers are always coprime to each other. For example, 7 and 11 are both prime, and they are coprime.
• Any two numbers that are right next to each other (consecutive integers) are always coprime. For instance, 8 and 9 are coprime.
• The number 1 is always coprime with any other number. This is because 1 only has one factor, which is 1 itself.
• If you have a prime number and another number that isn't a multiple of that prime, then those two numbers are coprime. For example, 7 (a prime) and 15 (not a multiple of 7) are coprime.
• The idea of coprime numbers usually applies to positive whole numbers.

Related pages

• Chinese remainder theorem
• Euler's totient function
• Euler's totient theorem

See also

In Spanish: Números coprimos para niños